WASHINGTON — President Trump on Monday signed a revised version of his executive order that would for the first time rewrite American immigration policy to bar migrants from predominantly Muslim nations, removing citizens of Iraq from the original travel embargo and scrapping a provision that explicitly protected religious minorities.

The order, which comes about a month after federal judges blocked Mr. Trump’s haphazardly executed ban in January on residents from seven Middle Eastern and African countries, will not affect people who had previously been issued visas — a change that the administration hopes will avoid the chaos, protests and legal challenges that followed the first order.

But it did little to halt criticism from Democrats and immigrant rights groups, which predicted a renewed fight in the courts. Mr. Trump’s initial, hastily issued order on Jan. 27 prompted protests across the country, leaving tearful families stranded at airports abroad and in the United States.

The new measure will be phased in over the next two weeks, according to officials with the Department of Homeland Security.

John F. Kelly, the Homeland Security secretary, said the order was prospectiveg and applied only to foreign nationals outside of the United States who do not have a valid visa.

If you have a current valid visa to travel, we welcome you,g said Mr. Kelly, appearing alongside Secretary of State Rex W. Tillerson and Attorney General Jeff Sessions at the Ronald Reagan Federal Building in Washington early Monday — before leaving without taking reporters’ questions.

Unregulated, unvetted travel is not a universal privilege, especially when national security is at stake,g Mr. Kelly added.

The indefinite ban on refugees from Syria also has been reduced to a 120-day ban, requiring review and renewal.

Mr. Trump signed the first ban with great fanfare, in front of reporters at the Pentagon. We don’t want them here, Mr. Trump said of terrorists. We want to ensure that we are not admitting into our country the very threats our soldiers are fighting overseas. We only want to admit those into our country who will support our country, and love deeply our people.

This time, he signed the order in private, with the White House releasing a photograph of the seldom-silent president doing so alone at his desk in the Oval Office.

His staff offered no explanation for the lower-key rollout this time. But administration officials said the president wanted to emphasize that the rewrite was a collective effort, not like the secretive one by the White House advisers Stephen K. Bannon and Stephen Miller that resulted in the botched execution of the first order.

Justice Department lawyers said the revisions rendered moot legal cases against the original travel ban.

But opponents said that the removal of a section that had granted preferential treatment to victims of religious persecution — a provision that immigrant rights attorneys argued was intended to discriminate against Muslims — was a cosmetic change that did nothing to alter the order’s prejudicial purpose.

This is a retreat, but let’s be clear — it’s just another run at a Muslim ban, said Omar Jadwat, director of the Immigrants’ Rights Project at the American Civil Liberties Union, one of the groups that sued to stop the first order.

At its core, the second order looks very similar to the first, and I expect it will run into the same problems from the courts and the public that the first one did. They can’t unring the bell.

The Senate Democratic leader, Chuck Schumer of New York, described the new order as a watered-down ban that was still meanspirited and un-American.

Margaret Huang, executive director of Amnesty International USA, said in a statement that the new order would cause extreme fear and uncertainty for thousands of families by, once again, putting anti-Muslim hatred into policy.